Advertisements
Advertisements
Question
A body of mass 0.5 kg travels in a straight line with velocity v = a x3/2 where a = 5 m–1/2s–1. The work done by the net force during its displacement from x = 0 to x = 2 m is ______.
Options
1.5 J
50 J
10 J
100 J
Advertisements
Solution
A body of mass 0.5 kg travels in a straight line with velocity v = ax3/2 where a = 5 m–1/2s–1. The work done by the net force during its displacement from x = 0 to x = 2 m is 50 J.
Explanation:
Given, v = ax3/2
m = 0.5 kg, a = 5 m–1/2s–1, work done (W) = ?
We know that
Acceleration `a_0 = (dv)/(dt)` = `v (dv)/(dx) = ax^(3/2) d/(dx) (ax^(3/2))`
= `ax^(3/2) xx a xx 3/2 xx x^(1/2)`
= `3/2 a^2x^2`
Now, Force = `ma_0 = m 3/2 a^2x^2`
Work done = `int_(x = 0)^(x = 2) Fdx`
= `int_0^2 3/2 ma^2x^2dx`
= `3/2 ma^2 xx (x^3/3)_0^2`
= `1/2 ma^2 xx 8`
= `1/2 xx (0.5) xx (25) xx 8`
= 50 J
APPEARS IN
RELATED QUESTIONS
When you hold a pen and write on your notebook, what kind of force is exerted by you on the pen? By the pen on the notebook? By you on the notebook?
List all the forces acting on the block B in figure.
When Neils Bohr shook hand with Werner Heisenberg, what kind of force they exerted ?
Let E, G and N represent the magnitudes of electromagnetic gravitational and nuclear forces between two electrons at a given separation. Then
The sum of all electromagnetic forces between different particles of a system of charged particles is zero
A 60 kg man pushes a 40 kg man by a force of 60 N. The 40 kg man has pushed the other man with a force of
Which of the following systems may be adequately described by classical physics ?
(a) motion of a cricket ball
(b) motion of a dust particle
(c) a hydrogen atom
(d) a neutron changing to a proton.
At what distance should two charges, each equal to 1 C, be placed so that the force between them equals your weight ?
Two charged particles placed at a separation of 20 cm exert 20 N of Coulomb force on each other. What will be the force of the separation is increased to 25 cm?
The force with which the earth attracts an object is called the weight of the object. Calculate the weight of the moon from the following data : The universal constant of gravitation G = 6.67 × 11−11 N−m2/kg2, mass of the moon = 7.36 × 1022 kg, mass of the earth = 6 × 1024 kg and the distance between the earth and the moon = 3.8 × 105 km.
In tug of war, the team that exerts a larger tangential force on the ground wins. Consider the period in which a team is dragging the opposite team by applying a larger tangential force on the ground. List which of the following works are positive, which are negative and which are zero?
(a) work by the winning team on the losing team
(b) work by the losing team on the winning team
(c) work by the ground on the winning team
(d) work by the ground on the losing team
(e) total external work on the two teams.
The magnetic force on a charged particle is always perpendicular to its velocity. Can the magnetic force change the velocity of the particles? Speed of the particle?
A block of weight 100 N is slowly moved up a smooth incline of inclination 37° by a person. Calculate the work done by the person in moving the block through a distance of 2 m, if the driving force is (a) parallel to the incline and (b) in the horizontal direction.
A particle of mass m moves on a straight line with its velocity varying with the distance travelled, according to the equation \[\nu = a\sqrt{x}\] , where a is a constant. Find the total work done by all the forces during a displacement from \[x = 0 \text{ to } x - d\] .
A block of mass 2 kg kept at rest on an inclined plane of inclination 37° is pulled up the plane by applying a constant force of 20 N parallel to the incline. The force acts for one second. Find the work done by the force of gravity in that one second if the work done by the applied force is 40 J.
The 200 m free-style women's swimming gold medal at Seoul Olympics in 1988 was won by Heike Friendrich of East Germany when she set a new Olympic record of 1 minute and 57⋅56 seconds. Assume that she covered most of the distance with a uniform speed and had to exert 460 W to maintain her speed. Calculate the average force of resistance offered by the water during the swim.
In a children's park, there is a slide which has a total length of 10 m and a height of 8⋅0 m . A vertical ladder is provided to reach the top. A boy weighing 200 N climbs up the ladder to the top of the slide and slides down to the ground. The average friction offered by the slide is three tenth of his weight. Find (a) the work done by the ladder on the boy as he goes up; (b) the work done by the slide on the boy as he comes down. Neglect any work done by forces inside the body of the boy
A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 30° by a force of 10 N parallel to the inclined surface (Figure). The coefficient of friction between block and the incline is 0.1. If the block is pushed up by 10 m along the incline, calulate
- work done against gravity
- work done against force of friction
- increase in potential energy
- increase in kinetic energy
- work done by applied force.
A block of mass m is taken from A to B slowly under the action of a constant force R Work done by this force is ______.
If a force varies linearly with displacement, the area under the F-s graph forms:
